Hebrews reverses Jeremiah's "new covenant" saying "In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away." (Hebrews 8:13).
This is supposedly Paul referencing the prophet Y'rmiyahu / Jeremiah -- yet read the T'nach for yourself for it says the exact opposite of what Paul tells his readers. Y'rmiyahu / Jeremiah 46:27-28 says: "You fear not, O Jacob My servant, and be not dismayed, O Israel! for behold, I will redeem you from afar and your children from the land of their captivity, and Jacob shall return and be quiet and at ease, and there shall be none who disturb his rest. You fear not, My servant Jacob, says the L-rd, for I am with you, for I will make a full end of all the nations where I have driven you, but of you I will not make a full end, but I will chastise you justly, and I will not completely destroy you."
The translation “new” at the end of Y'rmiyahu / Jeremiah 31:30 (the Christian number is 31) really means “renewed” because verse 32 (33 in Christian versions) clearly states that the “new” b'rit (covenant) is going to be G-d’s Torah -- just as the Sinaic covenant is G-d's Torah. "For this is the covenant that I will form with the house of Israel after those days, says the L-rd: I have put (נָתַֽתִּי / “I have put") My Torah (תּֽוֹרָתִי֙ / Torati) among them, and I will inscribe it upon their hearts, and I will be their G-d and they shall be My people." Each covenant builds on the previous -- none "does away" with, vanishes or "grows old" as says Hebrews.
Translating חֲדָשָׁה at the end of verse 30 as "new" is incorrect and ought to be “renewed”, because verse 32 clearly states that the “new” b'rit (covenant) is going to be G-d’s Torah -- just as the Torah is the covenant of Sinai. This is a renewal of the earlier covenant. It is different from the previous b'rit (covenant) in one way only: Israel (Jews) broke the previous covenant, but we will not do this when the messiah comes and we enter the messianic age. This is because there will be a global knowledge of G-d and no one will need to be taught about G-d or about being good people -- it will be part of each of us.
Most translations of Y'rimayahu / Jeremiah 31:32 has "I shall put my Torah among them" -- but this is a mistranslation. The literal text is נָתַֽתִּי אֶת־תּוֹרָתִי בְּקִרְבָּם (“I have put My Torah among them”), -- the verb נָתַֽתִּי is in the past tense. The verb נָתַֽתִּי natati is the simple past tense and means I HAVE PUT (the future tense form “I shall put” would have to be אֶתֵּן ĕttén, which occurs 79 times in the T'nach).
If it is past tense it can't be about Jesus. Jesus hadn't been born yet. G-d is saying that His Torah was already given to the Jewish nation, and that this renewal of the covenant will be different in that in the days of the messiah Jews will no longer stray after idolatry (including Christianity).
If this is a "new" covenant were about Jesus why is G-d saying in this passage that He has already put the Torah among the Jews?
Why is He saying that this Torah will be inscribed in our hearts when the messiah comes -- when Christianity does not follow the mitzvot of the Torah, but states that Jesus "replaced" the need to keep kosher, and perform the other mitzvot? Hebrews changed the word of G-d and actually reverses it!
If this were about Jesus, why is the Torah not inscribed in the heart of every Jew alive today -- and clearly there are Jews who become atheists, even Christians or Muslims! Ergo Jesus did not fulfill this prophecy of Jeremiah -- and the "new" covenant is not Christianity.
It is a fundamental principle of Judaism that the Torah received at Sinai will never be changed nor become obsolete. This concept is mentioned in the Torah no less than 24 times, with the words: "This is an eternal law for all generations" (Sh'mot / Exodus 12:14, 12:17, 12:43, 27:21, 28:43, Vayikra / Leviticus 3:17, 7:36, 10:9, 16:29, 16:31, 16:34, 17:7, 23:14, 23:21, 23:31, 23:41, 24:3, Bamidbar / Numbers 10:8, 15:15, 19:10, 19:21, 18:23, 35:29, D'varim / Deuteronomy 29:28).
Rabbi Tovia Singer discusses distortion in Hebrews regarding the "new" covenant in the following YouTube video:
The covenant G-d made with us Jews is ETERNAL. Hebrews in the Christian bible lies about that. (B'reshit / Genesis 17:7): This shall be My covenant in your flesh, an eternal covenant.
There are many covenants -- and each one builds on the previous. G-d makes a promise to Noah that He will never again destroy mankind with a flood -- this is the promise of the Noachide covenant. G-d makes a series of promises to Abraham including בְּרִית בֵּין הַבְּתָרִים -- the covenant between the parts. This was the first of a series of promises G-d made to Abraham which culminated in the בְּרִית מִילָה (brit milah) found inB'reshit / Genesis 17 -- where we are told that בְּרִית מִילָה will be an eternal agreement between G-d and the Jews that Jews will show via the covenant of circumcision.
Missionaries who wish to argue that בְּרִית מִילָה is not included in G-d's covenantal promises to Jews ignore the Jewish bible itself. G-d says He will never desert the Jews. NEVER. Shoftim / Judges 2:1 "I will not break my covenant with you FOREVER."
G-d promises to punish the Jews for our sins -- but NOT to reject us. Y'rmiyahu / Jeremiah 46:27.
"You fear not, O Jacob My servant, and be not dismayed, O Israel! for behold, I will redeem you from afar and your children from the land of their captivity, and Jacob shall return and be quiet and at ease, and there shall be none who disturb his rest. 28. You fear not, My servant Jacob, says the L-rd, for I am with you, for I will make a full end of all the nations where I have driven you, but of you I will not make a full end, but I will chastise you justly, and I will not completely destroy you."
T'hillim / Psalms 105:8-10 "He remembers His covenant forever, the word He had commanded to the thousandth generation, 9. Which He had made with Abraham, and His oath to Isaac, 10. And He set it up to Jacob as a statute, to Israel as an EVERLASTING COVENANT"
G-d repeatedly tells us that He will not break His covenant with Israel EVER. Here are just a few: Vayikra / Leviticus 26:44-45. "But despite all this, while they are in the land of their enemies, I will not despise them nor will I reject them to annihilate them, thereby breaking My covenant that is with them, for I am the L-rd their G-d. 45. I will remember for them the covenant [made with] the ancestors, whom I took out from the land of Egypt before the eyes of the nations, to be a G-d to them. I am the L-rd."
Y'chezkel / Ezekiel 16:59-60 "For so said the L-rd G-d: I have done with you as you did, that you despised an oath to violate a covenant. 60. But I shall remember My covenant with you in the days of your youth, and I shall establish for you an EVERLASTING COVENANT."
Hebrews completely distorted what the prophet Jeremiah said. Hebrews says G-d will divorce the Jews -- but G-d disagrees!
"Behold I will gather them (the Jews) from all the lands where I have driven them with My anger and with My wrath and with great fury, and I will restore them to this place and I will cause them to dwell safely. And they shall be My people, and I will be their G-d. And I will give them one accord and one way to fear Me all the time, so that it be good for them and for their children after them. And I will form for them an EVERLASTING COVENANT, that I will not turn away from them to do them good, and My fear I will place in their heart, not to turn away from Me." (Y'rmiyahu / Jeremiah 32:37-40).
Christians have been lied to about this as they have about so much. For additional information on the "new covenant" please read Jeremiah 31:30-36 - Will the Real "New Covenant" Please Stand Up!.